Functional equations on abelian groups with involution. II
type: Item
instance of: scholarly article
title: Functional equations on abelian groups with involution. II
zbMATH Open document ID: 0940.39020
published in: Aequationes Mathematicae
publication date: 2000-07-24T00:00:00Z
review text: The author continues his investigations started in the paper [Aequationes Math. 54, No. 1-2, 144-172 (1997; Zbl 0899.39007)]. Here, using again the fruitfull notion of \(K\)-spherical function, he solves the functional equation \[ f(x+y)+ f(x+\sigma y)= 2f(x)+ h_1(y)+ g(x)h_2(y), \quad x,y \in G, \] where \(\sigma:G\to G\) is an automorphism of the abelian topological group \(G\) such that \(\sigma^2=\text{id}\) and \(f,g,h_1, h_2:G\to \mathbb{C}\) are continuous. This functional equation contains as a special case for example Swiatak's equation \((h_1=\), \(h_2=g)\) or the quadratic equation \((h_1=2f\), \(g=h_2=0)\).
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1176812
zbMATH Keywords: involution
zbMATH Keywords: \(K\)-spherical function
zbMATH Keywords: abelian topological group
zbMATH Keywords: Swiatak's equation
zbMATH Keywords: quadratic equation
author: Henrik Stetkær
reviewed by: Jens Schwaiger
MaRDI profile type: Publication
full work available at URL: s000100050032
OpenAlex ID: W4241352367
DOI: 10.1007/S000100050032
description: scientific article; zbMATH DE number 1176812